The technically correct (the best kind of correct) answer to the question is 1 since 26, 32, 29, and 28 are all whole numbers and, as fractions, would all have a denominator of 1.
If you mean something like "what is the LCD of 1/26, 1/32, 1/29, and 1/28 ?" then:
26 = 2 * 13
32 = 2 * 2 * 2 * 2 * 2
29 = 29
28 = 2 * 2 * 7
It's like we're making a parts list with enough parts to make 26, 32, 29, or 28. In this case our parts list is 2 * 2 * 2 * 2 * 2 * 7 * 13 * 29 because that list has enough parts to make 26, 32, 29, 28.
2 * 2 * 2 * 2 * 2 * 7 * 13 * 29 = 84448
Answer: The LCD is 84448.